When Mrs. Norris is temporarily paralyzed after indirectly seeing the basilisk in Chamber Of Secrets and Filch at first believes she’s been killed, he breaks down into violent sobs. That is not how a grown man, particularly one as usually heartless as Filch, reacts to a dead cat. Once he finds out she’s only been petrified, he still viciously attacks Harry, who he believes to be responsible. No one outside of a Cathy comic has ever loved a cat more than Argus Filch.
But it actually gets weirder. To say that Mrs. Norris is an exceptionally smart cat would be like saying Superman is an exceptionally strong dude. Filch and Mrs. Norris often work as a team, patrolling different areas of the castle for misbehaving students. Getting caught by Mrs. Norris is as bad as getting caught by Filch, because she will fetch him straight away. This means that Mrs. Norris has memorized the school’s rules, understands them, and recognizes when a student is breaking them. In the first book, Hagrid tells Harry and Ron that he suspects Filch has trained Mrs. Norris to follow him specifically. You’ll recognize all of these as things cats can’t do. (It’s been theorized that Mrs. Norris might be part Kneazle, a cat-like magical creature with superfeline intelligence, but Rowling has shot it down.) She also shows up on the Marauder’s Map, while other animals don’t. It’s almost like she’s a person in the body of a cat in a magical universe where that exact thing can definitely happen.